The present invention relates to tomography, that area of technology which obtains an image of internal parts of an object in a plane through the object. In particular, the present invention relates to computerized tomography.
Computerized tomography (CT) refers to the procedures used to generate two dimensional maps of some physical quantity in a planar section of a target by measuring and analyzing the attenuation of beams of penetrating radiation passed through the target along sets of coplanar rays. As practiced, a complete apparatus must contain four elements: (1) a source of penetrating radiation, (2) detectors that measure the transmitted intensity of the radiation after passage through the target, and that can be calibrated also to give the unattenuated intensity of radiation in the absence of the target, (3) a computational device to store and process the attenuation measurements, converting them into a digital map of attenuation coefficients in the observed plane of the target, and (4) a device to display the resultant image.
Computerized tomography can be practiced in many ways, but the broadest commercial usage is in medical radiology to provide diagnostic maps of bone and tissue structure in human patients (see, Swindell, W. and H. H. Barrett, 1977, "Computerized Tomography: Taking Sectional X-Rays", Physics Today, pp. 32-41; Jaffe, C. C., 1982, "Medical Imaging", American Scientist, vol. 70, pp. 576-585; and Alexander, P., 1983, "Array Processors in Medical Imaging", Computer, vol. 16, pp. 17-30). Medical CT uses broad band bremsstrahlung X-ray tubes to produce penetrating radiation that is measured, typically, by scintillation crystals and photo-tubes. Measurements are stored in a programmable digital computer and analyzed using a method generically referred to as filtered (or convolution) backprojection (referred to hereafter as FBP). The density map derived from the analysis is displayed on a cathode ray tube as a two dimensional image containing perhaps 250.times.250 or 500.times.500 elements or pixels, with a resolution of about 1 millimeter, and 1% accuracy in determination of X-ray attenuation coefficient. However, special purpose tomography probes have been built using other types of radiation and detectors, such as gamma rays, and ultrasound.
The present method has applications to commercial medical CT and, in general, to any tomographic analysis, especially those where the image format contains large numbers of pixels. At present there is great interest across many industries to develop tomographic testing devices. In fact, the ability to handle routinely large format images could stimulate development of a new class of nondestructive testing apparatus based on tomography.
Several manufacturers including Picker, GE and EMI, produce medical CT scanners that are installed in thousands of hospitals throughout the US and world, at costs ranging from a few hundred thousand to a million or more dollars. CT apparatus have gone through several "generations" that involve basic changes in the scanning procedures and image format. Most data processing software is described in brochures as "proprietary". Processing speed of software is often used as a major selling point by the manufacturers. Observational strategies for data taking and processing are intimately coupled, but the devices do use general purpose programmable computers, in part. The method disclosed here dramatically reduces the image processing time. In current machines more time is spent analyzing data than collecting it, say 4 seconds to acquire the scan versus 30 seconds to process. Some recently described devices acquire data even more rapidly. A high speed processing capability would alter clinical practice of CT by allowing routine real time views of scans. Present practice is to obtain several scans, say 20 in adjacent planes of a patient, to complete a procedure, but to analyze only a few scans while the patient is present, in order to save time. Data analysis occurs at off-peak times, with images viewed by the radiologist at a later time. Also, there is no unique "best" way to reconstruct tomographic data. Radiologists choose from a menu of possible approaches depending on the procedure or feature being scanned. All approaches use the generic filtered backprojection method, but in different implementations chosen to highlight various features of the image. With our faster method such choices could be explored far more quickly, giving greater flexibility and insight to the physician. Thus, rapid reconstruction algorithms appear to be of commercial and diagnostic value to medical CT.
To generate accurate tomographic images, sufficiently noise-free data must be obtained along a sufficient number of independent coplanar paths through the target (See Shepp, L. A. and B. F. Logan, 1974, "The Fourier Reconstruction of a Head Section", IEEE Trans. Nucl. Sci., vol. NS-21, pp. 21-43). Observational paths can be labeled according to their view angle .phi. and impact parameter t.sub.1, with respect to coordinates fixed in the target, as shown in FIG. 1. The choice of paths on which to acquire data is somewhat arbitrary, but two methods are in common use. In medical tomography measurements are typically obtained with a fixed set of detectors located along a ring surrounding the patient, as shown in FIG. 2. The X-ray source rotates about the ring, illuminating a series of detectors opposite the source with a fan beam of radiation. The opening angle of the X-ray beam is broad enough so that the fan of paths from source to detector completely encompasses the target. For accurate reconstruction of the entire target, the range of impact parameters must span the diameter of the target and the angular rotations must span at least one half of a complete rotation. We refer to the mode of operation shown in FIG. 2 as fan beam geometry. In another acceptable mode of operation the target is illuminated along a set of parallel, coplanar paths at a series of view angles. We refer to this mode of operation as plane parallel geometry. FIG. 3 illustrates this type of illumination.
Along a specific path, labeled by its view angle and impact parameter, the detector measures the transmitted intensity I.sub.T (t.sub.1,.phi.). For analysis the measurement of transmitted intensity must be converted into a measure of beam attenuation, or optical depth, along the path, given by P(t.sub.1,.phi.)=1n[(I.sub.o (t.sub.1,.phi.)/I.sub.T (t.sub.1,.phi.)] where I.sub.o (t.sub.1,.phi.) is the intensity incident on the target before attenuation. P(t.sub.1,.phi.) is referred to as a "projection". The intensity of the unattenuated beam must be established by a separate calibration of the apparatus.
The goal of tomographic procedures is to convert the projection data into an image of the attenuation coefficient in the observed plane of the target. In its raw form the data simply provides shadow images of the target as viewed from many angles. It is not readily apparent how to locate or quantify absorbers in the plane of the target directly from the data. Only by using a reconstruction procedure can the data be combined to produce an image of the target. Thus, tomographic apparatus requires an inversion or reconstruction method.
In a typical commercial CT apparatus the reconstruction is produced in digital format and displayed as an image defined on a two dimensional grid containing, perhaps, 500 rows by 500 columns, or 250,000 elements. The data from which the image is reconstructed consist of a comparable, but even larger set of projection measurements. For this reason general purpose programmable digital computers or special purpose computers are used to store data, convert measurements of intensity to measures of attenuation, and to carry out the procedural steps of the reconstruction method.
Initial reconstruction methods for medical tomography used an iterative procedure (see U.S. Pat. No. 3,778,614). Starting with an arbitrary initial trial solution, the method computationally derived values for projection data that would occur from the trial image. Differences between the measured and derived projection data were used to correct the trial image successively, until sufficient agreement obtained between computed and observed projection.
Later the far better method of Convolution Backprojection, also referred to as Filtered Backprojection (FBP), was developed and applied in tomography apparatus (See Shepp, L. A. and B. F. Logan, 1974, "The Fourier Reconstruction of a Head Section", IEEE Trans. Nucl. Sci., vol. NS-21, pp. 21-43, and LeMay, C. A. G., 1975, U.S. Pat. No. 3,924,129). Filtered backprojection has become the universally practiced method for commercial tomographic reconstruction. FBP is better than the iterative method: first, because it can be demonstrated by mathematical analysis that FBP produces images that approximate the true image of the attenuation coefficient in the target, and second, because the computational effort required to invert the data using FBP is smaller than in the iterative method. With FBP the number of computational steps required to invert the data is known in advance, while with the iterative method the number of iteration cycles required to produce an acceptable image is not known in advance.
Furthermore, Shepp, L. A. and B. F. Logan, 1974, "The Fourier Reconstruction of a Head Section", IEEE Trans. Nucl. Sci., vol. NS-21, pp. 21-43, and Chesler, D. A., S. J. Riederer, and N. J. Pelc, 1977, "Noise Due to Photon Counting Statistics in Computed X-Ray Tomography", Journal of Computer Assisted Tomography, vol. 1, pp. 66-74 were able to analyze qualitatively the degree of noise amplification introduced by filtered backprojection. Real projection data are not measured with infinite accuracy. Noise in the data leads to noise in the reconstruction. The ratio between the relative accuracy of the reconstruction and the relative accuracy of the data defines the amplification factor. Typically, the amplification factor can be as large as ten for medical scale images. FBP methods allow one to assess the noise level required in the data to produce images of specified accuracy. The noise level in a FBP reconstruction can be lowered by incorporating low-pass filtering into the basic FBP algorithm. Filters allow noise levels to be adjusted, but at the expense of degrading resolution somewhat. Filtered reconstructions correspond to images that are averaged over neighboring regions in order to reduce noise, but the smoothing of noise results in lower resolution. Without filtering of some sort medical images tend to be unacceptably noisy.
The present invention includes the step of inversion of tomographic data that can be used to obtain images far more rapidly than is possible using filtered backprojection, while still producing images of comparable quality.